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TRAVELLING WAVE SOLUTIONS IN NONLOCAL REACTION–DIFFUSION SYSTEMS WITH DELAYS AND APPLICATIONS

  • ZHI-XIAN YU (a1) and RONG YUAN (a1)
  • DOI: http://dx.doi.org/10.1017/S1446181109000406
  • Published online: 01 March 2010
Abstract
Abstract

This paper deals with two-species convolution diffusion-competition models of Lotka–Volterra type with delays which describe more accurate information than the Laplacian diffusion-competition models. We first investigate the existence of travelling wave solutions of a class of nonlocal convolution diffusion systems with weak quasimonotonicity or weak exponential quasimonotonicity by a cross-iteration technique and Schauder’s fixed point theorem. When the results are applied to the convolution diffusion-competition models with delays, we establish the existence of travelling wave solutions as well as asymptotic behaviour.

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Corresponding author
For correspondence; e-mail: yuzx@mail.bnu.edu.cn
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